论文标题
离散动力学系统家族及其在分叉理论中的应用的弗雷霍姆理论
Fredholm theory of families of discrete dynamical systems and its applications to bifurcation theory
论文作者
论文摘要
在先前的工作中，我们证明了针对渐近双曲离散动力学系统家族的索引定理，并为分叉理论获得了应用。与渐近双波动性相比，弱和更常见的假设是指数二分法的存在。在本文中，我们将所有以前的结果推广到后一种环境，这需要对我们的论点进行重大修改。此外，我们将Nemitski操作员的连续性和可不同性的先前结果推广到离散动力学系统中，以获得更好的分叉结果。
In a previous work, we proved an index theorem for families of asymptotically hyperbolic discrete dynamical systems and obtained applications to bifurcation theory. A weaker and far more common assumption than asymptotic hyperbolicity is the existence of an exponential dichotomy. In this paper we generalize all our previous results to the latter setting, which requires substantial modifications of our arguments. In addition, we generalize previous results on continuity and differentiability of Nemitski operators for discrete dynamical systems to obtain even better bifurcation results.
